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Resonant Converter Control Loop Design Tutorial –December 2018-
Resonant Converter Control Loop Design
Tutorial –December 2018-
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General index 1. Introduction ........................................................................................3
2. AC Sweep Analysis ..............................................................................3
3. Control design in SmartCtrl ..................................................................5
4. Validation ............................................................................................9
Figure index Figure 1: AC analysis configuration .................................................................. 3 Figure 2: Circuit schematic including the AC sweep ............................................. 4 Figure 3: Frequency response of the resonant converter....................................... 4 Figure 4: SmartCtrl shortcut access.................................................................. 5 Figure 5: Exportation to SmartCtrl options window .............................................. 5 Figure 6: Transfer function imported ................................................................ 5 Figure 7: Plant transfer function fully imported ................................................... 6 Figure 8: Sensor definition ............................................................................. 6 Figure 9: compensator definition ..................................................................... 7 Figure 10: Solution map view ......................................................................... 7 Figure 11: SmartCtrl loop with all the elements fully defined.................................. 8 Figure 12: SmartCtrl loop solution ................................................................... 8 Figure 13: Kp and Ti values extracted from SmartCtrl .......................................... 9 Figure 14: Psim schematic including a input voltage step .................................... 10 Figure 15: Output voltage............................................................................ 10
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Resonant C onv erter C ontrol Loop Design V 3.0 – December 2018 www.powersmartcontrol.com
1. Introduction
SmartCtr is a general-purpose software specifically designed for power electronics application. This tutorial is intended to guide you, step by step, to design the control loop of a resonant converter.
Since the transfer function of a resonant converter is difficult to derive, one of the main purposes of this example is to illustrate that the resonant converter can be represented by the imported ac sweep results from PSIM, and the control loop of the resonant converter can be designed using SmartCtrl.
This example demonstrates the power and flexibility of using SmartCtrl in combination with PSIM to design the control loop of any power converters.
The first step is to obtain the resonant converter frequency response by means of the PSIM ac analysis.
2. AC Sweep Analysis
1. Perform ac analysis in PSIM
The frequency response of the plant is obtained directly from the circuit of the resonant converter using PSIM’s ac analysis, there is no need to generate an averaged model. The converter circuit is shown in Figure 2.
To perform the ac analysis, the ac sweep block, the ac source for signal injection and the AC probe are needed.
To configure the AC seep, use the parameters of Figure 1.
Figure 1: AC analysis configuration
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Resonant C onv erter C ontrol Loop Design V 3.0 – December 2018 www.powersmartcontrol.com
Figure 2: Circuit schematic including the AC sweep
After the simulation, the frequency response of the output voltage versus the control variable Ton is obtained, as shown in Figure 3. Once the frequency response is obtained, it can be imported into SmartCtrl.
Figure 3: Frequency response of the resonant converter
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Resonant C onv erter C ontrol Loop Design V 3.0 – December 2018 www.powersmartcontrol.com
3. Control design in SmartCtrl
1. Import the frequency response data into SmartCtrl
Click the SmartCtrl button shown in Figure 4 to open SmartCtrl. This action sends the frequency response data from the PSIM ac analysis to SmartCtrl. Enter the output voltage and the switching frequency and click OK to continue. See Figure 5.
Figure 4: SmartCtrl shortcut access
Figure 5: Exportation to SmartCtrl options window
The loaded transfer function is automatically plotted as shown in Figure 6.
Figure 6: Transfer function imported
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Resonant C onv erter C ontrol Loop Design V 3.0 – December 2018 www.powersmartcontrol.com
At this point, the plant is fully defined by the AC sweep import from Psim. The next step is to define the sensor and the regulator. See Figure 7.
Figure 7: Plant transfer function fully imported
Click in the sensor tab and select a “voltage divider” sensor topology. Type a reference voltage of 4.89uV and click in “calculate gain” button. See Figure 8.
Figure 8: Sensor definition
To configure the compensator click in “compensator tab”, select a PI compensator and parametrize it as shown in Figure 9.
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Figure 9: compensator definition
Once all the loop transfer elements are defined, the crossover frequency and the phase margin can be selected. SmartCtrl provides a guideline and an easy way of selecting the crossover frequency and the phase margin through the Solution Map.
Each point within the white area corresponds to a combination of cross freq. and phase margin that lead to a stable solution. In addition, when a point is selected, the attenuation given by the sensor and the regulator at the switching frequency is provided.
Note that not enough attenuation at the switching frequency could provoke high frequency oscillations.
To carry out the selection, click on the Set button and SmartCtrl will display the solutions map. Then left click a point within the white area, and click OK to continue. For this tutorial a cross freq of 4.235kHz and a phase margin of 72.6degrees have been chosen.
Figure 10: Solution map view
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Resonant C onv erter C ontrol Loop Design V 3.0 – December 2018 www.powersmartcontrol.com
Once the crossover frequency and the phase margin are selected, the solution map will be shown on the right side of the input data window. If, at any time, these two parameters need to be changed, just click on the shown solution map.
Figure 11: SmartCtrl loop with all the elements fully defined
Now accept the selected configuration and confirm the design, the program will automatically show the system performance in terms of the frequency response and transient response. Please, note that the solution map window is always present.
Figure 12: SmartCtrl loop solution
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Resonant C onv erter C ontrol Loop Design V 3.0 – December 2018 www.powersmartcontrol.com
4. Validation
1. Validate the control loop design
In order to check the closed loop performance of the regulator designed by SmartCtrl, a closed loop time-domain simulation is carried out in PSIM.
Two different designs are obtained from SmartCtrl. The following table shows the control loop bandwidth (BW) and the phase margin (PM) of these two designs, as well as the regulator parameters.
Design #1 Design #2
Bandwidth = 3.5kHz
Phase Margin = 55º
Bandwidth = 1kHz
Phase Margin = 90º
Kp = 1.198
Kint = 38.92u
Kp = 471m
Kint = 35.56u
Those values can be obtained from SmartCtrl as shown in Figure 13.
Figure 13: Kp and Ti values extracted from SmartCtrl
Using the two regulators from the table above, the corresponding closed loop responses are simulated in PSIM. PSIM schematic can be found in Figure 14. In this schematic, an input voltage step at 5ms has been added to test the dynamical response of the calculated compensator.
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Figure 14: Psim schematic including a input voltage step
It can be seen in Figure 15 the result of the simulation. The steady state output voltage is 400V, as it was specified and it can be seen how it is maintained even with an input step of 100V.
Figure 15: Output voltage
If this simulation is repeated but with the other values of the PI compensator (Kp = 471m / Kint = 35.56u) it can be observed from the waveforms that the first design
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(Design #1) tracks the reference signal more accurately than the second design (Design #2). Although Design #1 has a lower phase margin with under-damped oscillations, its higher bandwidth and higher low-frequency gain leads to a faster response.
This example shows that, SmartCtr l in combination w ith PSIM, with the capability to import frequency response results from PSIM, provide a fast and powerful platform for control loop design and optimization of any power converters.
